Author

Raphael Steiner

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Preprint Sep 2026

Asymmetric Homomorphism Thresholds for Graphs of Large Odd Girth

We determine the asymmetric homomorphism threshold from graphs of odd girth at least $7$ to triangle-free graphs, showing that $\delta_{\mathrm{hom}}(\{C_3,C_5\},\{C_3\})=\frac{1}{9}$. Equivalently, for every $\varepsilon>0$, every $n$-vertex graph of odd girth at least $7$ and minimum degree at least $(1/9+\varepsilon...

Romain Bourneuf, Raphael Steiner, Stéphan Thomassé et al. · 0 citations

Preprint Aug 2026

Proof of Lichiardopol's conjecture on disjoint directed cycles of distinct lengths

There is a fascinating array of interrelated questions studying which structures can be guaranteed in digraphs of large minimum out-degree. These often have intriguingly simple statements, yet seem surprisingly difficult to approach. A well-known example is Lichiardopol's conjecture (2014), stating that there exists a...

Sandra Albrechtsen, Raphael Steiner · 0 citations